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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2505.12037 |
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| _version_ | 1866912381017260032 |
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| author | Jiang, Jiashuo Zong, Yiming Ye, Yinyu |
| author_facet | Jiang, Jiashuo Zong, Yiming Ye, Yinyu |
| contents | Reinforcement learning (RL) problems are fundamental in online decision-making and have been instrumental in finding an optimal policy for Markov decision processes (MDPs). Function approximations are usually deployed to handle large or infinite state-action space. In our work, we consider the RL problems with function approximation and we develop a new algorithm to solve it efficiently. Our algorithm is based on the linear programming (LP) reformulation and it resolves the LP at each iteration improved with new data arrival. Such a resolving scheme enables our algorithm to achieve an instance-dependent sample complexity guarantee, more precisely, when we have $N$ data, the output of our algorithm enjoys an instance-dependent $\tilde{O}(1/N)$ suboptimality gap. In comparison to the $O(1/\sqrt{N})$ worst-case guarantee established in the previous literature, our instance-dependent guarantee is tighter when the underlying instance is favorable, and the numerical experiments also reveal the efficient empirical performances of our algorithms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_12037 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Adaptive Resolving Methods for Reinforcement Learning with Function Approximations Jiang, Jiashuo Zong, Yiming Ye, Yinyu Machine Learning Reinforcement learning (RL) problems are fundamental in online decision-making and have been instrumental in finding an optimal policy for Markov decision processes (MDPs). Function approximations are usually deployed to handle large or infinite state-action space. In our work, we consider the RL problems with function approximation and we develop a new algorithm to solve it efficiently. Our algorithm is based on the linear programming (LP) reformulation and it resolves the LP at each iteration improved with new data arrival. Such a resolving scheme enables our algorithm to achieve an instance-dependent sample complexity guarantee, more precisely, when we have $N$ data, the output of our algorithm enjoys an instance-dependent $\tilde{O}(1/N)$ suboptimality gap. In comparison to the $O(1/\sqrt{N})$ worst-case guarantee established in the previous literature, our instance-dependent guarantee is tighter when the underlying instance is favorable, and the numerical experiments also reveal the efficient empirical performances of our algorithms. |
| title | Adaptive Resolving Methods for Reinforcement Learning with Function Approximations |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2505.12037 |